#mathematical discovery

[frank-olivier]

Mathematics in the Age of Automation: Navigating the Opportunities and Challenges of AI

The convergence of Artificial Intelligence and mathematics, exemplified by the Alpha Proof project, heralds a transformative era for the field, yet its full potential remains contingent upon addressing inherent challenges. A recent conversation with key contributors provided invaluable insights into the application of AI in mathematical reasoning, proof verification, and discovery.

Alpha Proof's architectural lineage from Alpha Zero underscores the viability of Reinforcement Learning in navigating the vast mathematical search space, as evidenced by its solutions to a subset of International Mathematical Olympiad problems. However, the project's true transformative potential lies not merely in its problem-solving prowess, but in its capacity to facilitate collaborative mathematics by automating proof verification, thereby freeing human mathematicians to pursue more abstract and innovative endeavors.

A significant impediment to the widespread adoption of such AI tools is their inaccessibility to the broader mathematical community. The development of intuitive interfaces and educational resources, particularly in formal proof systems like Lean, is crucial for democratizing access to these technologies. By doing so, not only can the collaboration between humans and AI be enhanced, but also personalized learning experiences can be offered, thereby bridging the gap between computational mathematics and traditional mathematical practices.

The symbiotic relationship between human creativity and AI capabilities emerges as a pivotal theme. While AI excels in the structured realm of theorem-proving, human ingenuity remains indispensable in the more ephemeral domain of theory-building, where the selection of problems and the formulation of novel questions dictate the trajectory of mathematical progress. This dichotomy suggests a future where AI augments human capabilities, enabling a deeper exploration of mathematical truths, while humans continue to drive the creative impetus behind theoretical advancements.

Google's DeepMind's AlphaProof Team (No Priors, November 2024)

Friday, November 15, 2024

[capricorn-0mnikorn]

Vihart's Pi Day (3.14) rant for 2024: "folded circle snacks" [and convergent cultural evolution, re: cooking]

Proper closed captions in English. Fast narration. ~6 minutes.

One thing I like about folded circle sandwiches vs. the stacked square ones is that the filling is less likely to fall out when I try and pick it up.

[dearreader-12]

I've discovered two important women in STEM today!

Emmy Noether who was an outstanding mathematician who doesn't get enough credit for the work she did for the world of math and physics! She is the reason why in physics you learn that momentum is conserved for isolated systems, she discovered that!

Stephanie Kwolek who was the main inventor for Kevlar armor by finding the chemical compound that makes up the material of the armor. She also contributed to helping invent Spandex!

Imagine how many more achievements are still undiscovered to this day that could change the world as we know it. And now, women are more likely to be allowed to be involved in those discoveries! Shoot for the stars everyone, maybe you could be the one to discover something groundbreaking!

[pleuvoire]

i especially love learning about math throughout history because it is sooooo crazy to me how those ancient dudes were scribbling in quill pens on parchment the things you learn on your calculus exam. the stuff you do with high-powered graphing calculator online nowadays is the same exact thing dudes with no plumbing were doing by hand and by candlelight. some of our fundamental building blocks of mathematical theory come from TWO THOUSAND YEARS AGO. it feels like all of us throughout history are tapping into the same pure unchanging vein of the universe itself... like in sci-fi stories when there are ancient documents recording the existence of aliens that still walk among us today, except it’s REAL. soooooooooooooo cool

[rivenantiqnerd]

I love women in stem

do YOU 🫵 love women in stem??

[atsushis-missing-leg]

Somehow... I found math fun for a couple minutes.

[manoasha]

The Genius Who Changed Everything: Isaac Newton's Journey 🍎🌌

Early Days: Isaac Newton was born on January 4, 1643, in England. He grew up on a farm, but from a young age, everyone could see he was super smart. Big Achievements: Newton did some super cool stuff with numbers and science. His most famous work, “Philosophiæ Naturalis Principia Mathematica,” taught us about how things move and why stuff falls down. Imagine understanding why an apple falls from…

[jcmarchi]

Inside FunSearch: Google DeepMind’s LLM that Discovered New Math and Computer Science Algorithms

New Post has been published on https://thedigitalinsider.com/inside-funsearch-google-deepminds-llm-that-discovered-new-math-and-computer-science-algorithms/

Inside FunSearch: Google DeepMind’s LLM that Discovered New Math and Computer Science Algorithms

Discovering new science is one of the ultimate frontiers for AI.

Created Using DALL-E

In this issue:

An anaysis of Google DeepMind’s FunSearch, a model that was able to discover new algorithms in computer science and mathematics.

Discovering new science might be most complete Turing Test for the AI models. New scientific methods require complex reasoning skills, combining knowledge from many fields, constant experimentation and evaluation, and many other complex cognitive skills. Google DeepMind has been one of the AI labs pushing the frontiers of using AI to streamline our path to new scientific discoveries. Models such as AlphaGo has enabled the discovery of new proteins while AlphaTensor was able to improve classic matrix multiplication algorithms. Google DeepMind’s newest iteration in this area is FunSearch, a model that was able to create new mathematics and computer science algorithms.

FunSearch provides a clever approach to discover new algorithms by “thinking in code”. Essentially, FunSearch uses an LLM to generate computer programs based on a set of functions for a given problem and then uses an evaluator to prove the different solutions. The FunSearch named is derived from the fact that the model iteratively searches the function space.

Inside FunSearch

[evolooka]

As Tesla said, it's all about frequency and vibration.

[xtruss]

Michigan State Students Discover Traces of School's First Observatory Built in 1881

— August 14, 2023 | Juliana Kim | NPR

The exterior of MSU's first campus observatory, circa 1900. Michigan State University Archives and Historical Collections

When Stacey Camp, an anthropology professor at Michigan State University, learned there was a hard, impenetrable surface underground north of campus, she assumed it was just a large rock.

But historic maps hinted at something bigger. After careful digging, her team of campus archeologists unearthed parts of a foundation that once belonged to the university's original observatory.

"What's exciting about this particular find is that it tells the story of how our campus and how higher education has changed so radically over time," Camp said.

The foundation of school's first observatory. The discovery gives insight into how scientific observation, as well as life on campus, has changed since the original observatory was built in 1881. Nick Schrader

The former observatory was built in 1881 by Rolla Carpenter, a former student and professor who taught a host of topics from mathematics, astronomy and French. He advocated for an observatory after the university acquired its first telescope. At the time, students would observe the sky on the roof of a campus building.

Fast forward to this past May, 142 years later. Construction workers were drilling hammock posts outside a residence hall when they hit something unusually hard beneath the ground. The crew later phoned the school's Campus Archaeology Program, tasked with investigating and preserving buried archaeological sites discovered accidentally on campus.

The program's staff cross-referenced the location with historic maps, which suggested that it was in same area of the university's first observatory.

"That could have been easily dismissed if we hadn't had some historic maps and knowledge of that area," said Camp, who is the director of the program.

A group of undergraduate and graduate students spent the next several weeks documenting, digging and excavating around the site until it became clear that the curious impenetrable surface was indeed the foundation of a previous school building.

MSU Campus Archaeology students dig up the first observatory located on Michigan State's campus, next to Wills House, June 8. Nick Schrader

On Monday, results from a ground-penetrating radar survey revealed that most of the foundation is intact. According to Camp, its condition is a "miracle" given all the changes and construction that have taken place on campus.

"You've got a sidewalk next to it. You've got a road there. You've got a dormitory, a basketball court," she said. "All of that has destroyed a lot of our historic space on campus."

The discovery was especially special for Levi Webb, a rising senior studying astrophysics and anthropology.

Webb did not know about the former observatory before he joined the archaeology project. The search left him wondering about the students who frequented the space and their shared interest in astronomy.

"Each of these people had a life just as vibrant as mine," he said. "That's all it takes, a little discovery to unearth this complete, complex history."

Individuals pose outside of the school's first observatory, circa 1888. The observatory is located behind where Willis House now stands on MSU's campus, just south of Grand River in North Neighborhood. Michigan State University Archives and Historical Collections

The project also was a boon for Webb's job at the current observatory. During a recent tour, Webb shared what his team uncovered and the differences between the old and new buildings.

"We have always talked about the history of the current observatory, which was built in 1969," he said. "But now, I can enrich that with, this has gone back even farther than 1969, all the way back to 1880."

Next summer, the program is expected to run a larger excavation project to uncover more of the foundation and possible artifacts along the way.

[floralfemmes]

was talking to my mom about how white people ignore the contributions of poc to academia and I found myself saying the words "I bet those idiots think Louis Pasteur was the first to discover germ theory"

which admittedly sounded pretentious as fuck but I'm just so angry that so few people know about the academic advancements during the golden age of Islam.

Islamic doctors were washing their hands and equipment when Europeans were still shoving dirty ass hands into bullet wounds. ancient Indians were describing tiny organisms worsening illness that could travel from person to person before Greece and Rome even started theorizing that some illnesses could be transmitted

also, not related to germ theory, but during the golden age of Islam, they developed an early version of surgery on the cornea. as in the fucking eye. and they were successful

and what have white people contributed exactly?

please go research the golden age of Islamic academia. so many of us wouldn't be alive today if not for their discoveries

people ask sometimes how I can be proud to be Muslim. this is just one of many reasons

some sources to get you started:

but keep in mind, it wasn't just science and medicine! we contributed to literature and philosophy and mathematics and political theory and more!

maybe show us some damn respect

[xcookedxchroniclesx]

Here's my basics to upwards math. It can get incredibly complex if you let it. It doesn't have algebra yet or subtraction. I think it is a more precise math because you are going upwards so all you do is add to get to your number while downwards you have to subtract from the higher definitive value down to your number. Downwards math eventually ends to, not upwards.

[memoriallibrarytmc]

What’s Here Wednesday: Collection Discovery, Math in Children’s Literature

The word “mathematics” might might some people groan or recoil in terror, but it can be a lot of fun if you teach it using an engaging book! The TMC’s Collection Discovery feature has a whole collection devoted to math in children’s literature. Specific math concepts are highlighted, such as geometry or fractions, but there are also sections on math in the “real world”, as well as diverse options. The books highlighted range from those that explicitly teach a concept... to those that are less “mathy”, teaching these topics in a relatable, less heavy-handed way. Teaching math CAN be a lot of fun... you just have to know where to look!

[fiction-quotes]

“It was just a little puzzle,” he wound say, “a game”; and his tone sounded more sad than modest. “The person who made the problem already knew the answer. Solving a problem for which you know there's an answer is like climbing a mountain with a guide, along a trail someone else has laid. In mathematics, the truth is somewhere out there in a place no one knows, beyond all the beaten paths. And it's not always at the top of the mountain. It might be in a crack on the smoothest cliff or somewhere deep in the valley.”

 —   The Housekeeper and the Professor (Ogawa Yōko)

[imgae-insertshockedgasps-16]

humans are space orcs

imagine someone with chronic joint pain, whose dream their whole lives has been to go to space and meet the aliens and be a scientist and learn

so they look up the requirements as a kid and go "fuck."

they wouldn't make the cut.

their dreams are dashed. hopes ruined. lifelong dre destroyed.

except....

they've never really said a whole lot about their pain. they don't particularly like doctors, and they think that they've been managing just fine, so they never saw the point.

so maybe... maybe if they just don't say anything, they can make it to space.

they spend all of their time training. doing physical therapy exercises so that their joints aren't so loose, soaking up as much scientific and mathematical knowledge as they can, teaching themselves to push through the worst of it in pursuit of their dream.

and they make it.

they make it to space! it was gruelling, tortuous work, but they made it!

their first mission is an exploratory one, with a diverse crew which only has one other human.

they're thrilled.

they have dozens of alien friends and acquaintances. they spend hours learning and researching alien planets and cultures. it's everything they've ever wanted!

but

it's exhausting.

they're in more pain than they've ever been, more frequently than they ever have.

they keep up their exercises as best they can, but even those are often too much.

they smile when asked if they're alright, tell everyone that "i'm fine! just tired."

but they need a break. they can't imagine going or being sent back to earth, this is their home now, with these people, on this ship. but they don't know how much longer they can take this.

one day, on their day off, a fellow researcher comes and knocks on their door.

"are you here?"

"not today islith."

"but we've been called! there are some exciting new discoveries that need further cataloging and investigation, and carlmoth thought you would enjoy the task!"

"i can't today, islith."

"are you ill?"

"...kind of? but i'll be right as rain tomorrow. it's my day off anyhow."

"nonsense! you should go down to medbay!"

"i'm alright, i promise."

"you get out here right this minute or i'll report you to medbay myself!"

"no!" there's a series of crashes and thumps, and then they open the door.

"oh, you look awful. come on, you really must need medbay, what if you're contagious." islith tries to grab them but they shy away.

"i'm not contagious, i promise."

"how can you possibly know that? what if you picked it up from a sample, or, or, garfon has been sick recently! humans can't survive cerian sicknesses-"

"i didn't catch something from garfon, islith," they sigh and open the door wider. "come in and let me explain."

"alright, but if i think you should go to medbay afterwards then i'm taking you there."

"sure, islith."

islith enters, notices the piles of clothes, rumpled bedsheets, the lights are off and the port window shut.

"what's wrong?"

they sigh again, "my body doesn't work like it's meant to, islith."

islith is wildly alarmed, "and you said there was no need for medbay?!? come with me right now and-"

"no! i can't, islith, you don't understand."

"then explain it to me."

"i've... always been this way, although it's gotten worse as i've gotten older. my body, it just isn't built quite right, there's something wrong with it that makes it not work properly and hurt often."

"you're right, i don't understand. why can't you go to medbay?"

"i'd... be thrown off the ship."

"what?!?"

and so they tell islith a story about a young child whose dream was to touch the stars.

"and now, it's too late. i'd get in huge trouble for lying to the government, especially for so long."

"well- but- but humans are so resilient! you hear all the stories!"

"not every human is the same, islith. some of us are born disabled, and some of us get hurt in accidents, just like any other species."

"well, then, well there must be something we can do?"

they look up in shock, "we?"

"of course we, you ridiculous creature," islith said with a fond sigh. "you didn't think i'd leave you to suffer, would you?"

"but, you could get in so much trouble!"

"that's alright, i don't mind. what else are friends for? and, anyway, we don't have to tell your government, we can tell mine."

"but i'll-"

"we don't have any rules like that. any of us who are disabled can still manage in space just fine with the right support, and i bet you could too."

"i- islith- i don't-"

"don't worry, we'll all back you when it comes down to it. you're out teammate, our family. no one on this ship wants to watch you leave because of something you can't control. now come on, let's talk to glidlep in medical, she'll understand."

and for years, things continued on that way, until eventually it was an open secret that the human with the exosuit was disabled and not technically allowed onboard.

and down the line, when nasa found out and was furious, the entire ship and more stood by their side.